ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D

□ABCDis a rectangle ...given∴All the angles are equal to90∘...by definition∴∠A=∠C=90oSo,∠A2=∠C2=45o.. (ACbisects∠Aas well as∠C)So,∠x=∠y=∠z=∠w=45o(i)In△ADC,∠x=∠yAD=CDfrom (i) and converse of isosceles triangle theoremSo,□ABCDis a square (ii) Diagonals bisect the angles in a square.⇒BDbisects∠Bas well as∠D. from(i)